AutoSamplingTheory.SALD.cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Dag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Dag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

Ordered data items

1. id : String (explicit)

   Stable plan-node identifier.

   ASTIS.SALD.cycle197.lower_2_packet.normalized_remainder_bound_def_source_gap

   interface : String (explicit)

   Text describing intended mathematical interface.

   Typed source-cited boundary: hNormalizedRemainderBoundDef is blocked on a paper definition or source-backed theorem identifying the scalar dominating bound as remainderBoundC phi x i * z^2. The existing cycle-196 integrability bridge is not repeated.

   source : AutoSamplingTheory.SourceAnchor (explicit)

   Source pointer.

   AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteEmSource — audited data reference, not expanded and not a compiled dependency edge

   targetLean : String (explicit)

   Textual planned implementation destination.

   AutoSamplingTheory/SALD.lean

   dependsOn : List String (explicit)

   Declared input names as strings, default empty.

   Ordered data items

   1. SALD.cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Obligation
   2. hNormalizedRemainderBoundDef
   3. remainderBound
   4. remainderBoundC
   5. SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound
   6. AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound
   7. appendix.tex:958-996
   8. appendix.tex:1161-1170
   9. appendix.tex:1358-1387
   10. appendix.tex:1422-1434
   11. source_contract_gap_missing_remainder_bound_definition

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. hNormalizedRemainderBoundInt
   2. hRemainderBoundInt
   3. Taylor-DCT package
   4. sald.general_moving_target_discrete.em_interpolation_fp
   5. sald.general_moving_target_discrete.kl_derivative
   6. divergence/FI/IBP handoff

   status : AutoSamplingTheory.ProofStatus (explicit)

   Recorded workflow status, default planned.

   AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

def cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Dag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle197.lower_2_packet.normalized_remainder_bound_def_source_gap"
      interface := "Typed source-cited boundary: hNormalizedRemainderBoundDef is blocked on a paper definition or source-backed theorem identifying the scalar dominating bound as remainderBoundC phi x i * z^2. The existing cycle-196 integrability bridge is not repeated."
      source := saldGeneralMovingTargetDiscreteEmSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle197GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoNormalizedRemainderBoundDefLower2Obligation",
        "hNormalizedRemainderBoundDef",
        "remainderBound",
        "remainderBoundC",
        "SALD.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound",
        "AutoSamplingTheory.TechnicalLemmas.SALDExtracted.selectedWeakTestNormalizedRemainderBoundIntOfQuadraticBound",
        "appendix.tex:958-996",
        "appendix.tex:1161-1170",
        "appendix.tex:1358-1387",
        "appendix.tex:1422-1434",
        "source_contract_gap_missing_remainder_bound_definition"
      ]
      reusedBy := [
        "hNormalizedRemainderBoundInt",
        "hRemainderBoundInt",
        "Taylor-DCT package",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "divergence/FI/IBP handoff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 198 lower_2: frozen Brownian event-field coordinate-sum source gap -/

/-- Cycle-198 lower_2 packet for the frozen Brownian event-field coordinate sum.

The existing cycle-160 assembly theorem consumes
`hFrozenScalarBrownianItoEventFieldCoordinateSum` as a source input; it does
not define the abstract `emGeneratorLaplacianEventField`.  Local inspection
therefore cannot unfold that field to a finite sum of
`brownianCoordinateGenerator` contributions.  This obligation records the
smaller source-cited blocker instead of adding a theorem that assumes the same
coordinate-sum equality under another name.
-/